GNNs generalizing neural networks for graph data have already been shown great success for various real-world applications. There are two streams in GNNs model design, i.e., spectral-based and spatial-based. Spectral-based GNNs provide graph convolution definition based on graph theory, which is utilized in GNN layers together with feature transformation [1]}, [2]}, [3]}. Graph convolutional networks (GCN) [4]} simplifies spectral-based GNN model into spatial aggregation scheme. Since then, many spatial-based GNNs variant are developed to update node representation via aggregating its neighbors' information, including graph attention network (GAT) [5]}, GraphSAGE [6]}, SGC [7]}, APPNP [8]}, et al [9]}, [10]}. Graph signal denoising is another perspective to understand GNNs. Recently, there are several works show that GCN is equivalent to the first-order approximation for graph denoising with Laplacian regularization [3]}, [12]}. The unified optimization framework are provided to unify many existing message passing schemes [13]}, [14]}.
